In Hamlet, does the title character gain understanding about himself or does he remain ignorant of his character flaws?
By Act 5, I see a big change in Hamlet's understanding of the difference between the things he can control and things he cannot -- and once he realizes that there are all kinds of things that are out of his control, he frees himself to act as he needs to. When he is speaking to Horatio he says "there is a Divinity that shapes our ends rough hew them how we will." I think this is great thought. We all "rough hew" our lives by the choices we make and the actions we take, but there a more "fate, chance, Providence, destiny" events that we can't control. For example, we can work hard in school and take challenging classes to improve our college application, but we can't control what a college admissions office is going to do. All we can do is the best we can. Hamlet realizes that he can't control all of the circumstances around Claudius, but he can be ready to take action and vengeance when the chance arrives.
What a great question! You are going to receive plenty of different answers to this question. I think the biggest character flaw that Hamlet suffers from during the course of the play is procrastination. He has opportunities to avenge his father, but does not take them through fear of the Ghost being untrue and also through fear that killing Claudius while he was at prayer would send him straight to heaven rather to hell where he might suffer. However, I do believe we see Hamlet as a character develop through the play, and in particular, Act V scene 1 is a key part of the play to focus on. Having returned from his abortive voyage to England, Hamlet seems ready to act and to accept the consequences of his actions, whatever fate has decreed for him. In Act V scene 1 we see him contemplating death and how even the most mighty of people share a common fate as they return to dust:
Imperial Caesar, dead and turn'd to clay.
Might stop a hole to keep the wind away.
O, that that earth, which kept the world in awe,
Should patch a wall, t'expel the winter's flaw.
We see in this scene therefore Hamlet's acceptance of the eventual destiny of all of us, even the greatest like Caesar, "who kept the world in awe," is now doomed to patching a wall in his state of earth. It is thus highly significant that when Hamlet jumps into Ophelia's grave, he declares himself to be "Hamlet the Dane." This new self-identification involves an acceptance of whatever fate can throw at him and also a determination to finally act in a way that he has not acted so far in the play. Therefore, I think the play demands a more complex interpretation of how Hamlet develops and gains self-understanding during the course of the play.